Is a non-relativistic approximation possible for the internal dynamics of "elementary" particles?

G. Morpurgo
1965 Physics Physique Fizika  
It is pointed out that, contrary to what it is usually implied, the internal dynamics in a compound model of an "elementary" particle is not necessarily relativistic. If the force which binds the constituent objects has a finite range and is not too singular, the relativistic character of the internal motion only depends on the range of such force and on the mass of the constituent particles, not on the depth of the potential well. For instance, for a quark antiquark model of the octet bosons
more » ... th a quark mass of 5 GeV and a range of the binding force (5m~)-1 , one has (p/M) 2 = 1/40, a non-relativistic situation quite similar to that occurring in nuclei. Starting from this observation it is pointed out that several features of the SU 3 and SU 6 dynamics can be understood by writing a non-relativistic Hamiltonian for quarks, in a way similar to that which is used in writing an Hamiltonian for a nucleus. More precisely: (1) one can understand why the Gell Mann-Okubo SU 3 mass formula for baryons works much better than its perturbative derivation would imply; (2) one can obtain the -3/2 ratio between the magnetic moments of proton and neutron, due to su6, by a very simple calculation, which, at the same time exhibits how peculiar is the situation f or the absolute values of the magnetic moments; some interesting aspects of the situation, though implied in the conventional derivation, are masked there under the algebra; (3) the point of view taken in this paper leads to the conclusion that su6 should possibly be valid only at non-relativistic energies of the interacting particles.
doi:10.1103/physicsphysiquefizika.2.95 fatcat:khkfpl4bjbdf3dqa7zqqezjpzu